How do you know that Water isn't supposed to boil at 90 degrees and every time god stops it from boiling till it gets to 100. This seems pretty unreasonable but its not provably false, and its certainly not experimentally verifiable. So here is an example of something that could be true if a divine being were to exist that could not be shown by science. This also covers the non-interference problem, as if some divine being interferes in 100% of the experiments scientific truth could be entirely wrong.

As for truth, type matters. If you go with a radical doubt approach, its difficult to know much more than your own existence, because you can't prove that you aren't being deceived about the world. You can't even prove that people other than you exist. This is covered extensively in Philosophy, largely coming from the work of Descartes, but revisited by others. Other, more rational approaches start from different axioms and derive different results. In particular, the scientific method itself requires certain axioms.

Furthermore, no one has proven anything beyond a reasonable doubt in science, new experiments change and expand on previous laws. Even something as basic as gravity could behave radically differently from what was previously thought for something as yet untested. For instance, the gravity between two objects whose relative velocity is greater than the speed of light. For all we know the theory of gravity might be a tiny special case of the general picture. No experiment has proven it to be the be all and end all, just like no "god measuring" experiment would have a final word.

As for the 7 step argument Thorne postulates, step 4/5/6/7 is invalid as you have already assumed no gods, and consistency of one assumption does not imply the inconsistency of another.

1. Assume there are gods.
2. Do our models and theories of the universe still apply?
3. Yes, they do.
4. Then there probably are gods.
5. Is there evidence for gods?
6. Gods exist by assumption 1 so in this theory absolutely.
7. Then to the best of our knowledge there are gods.

If one of these theories was inconsistent or created problems it would be easy to reject it, but both are valid so someone needs to devise an experiment to show one or the other to be incorrect before outright rejecting either. In other words, neither "God exists." nor "God does not exist." is a statement of science, much like neither "The flying spaghetti monster exists." not "The flying spaghetti monster does not exist." is a statement of science. When we reject these things as implausible we aren't using scientific evidence we are making hypotheses from the entirety of our entire life experience about the plausibility of something we can't verify.

If I believe P is not equal to NP, I'm not asserting that computer science shows P is not equal to NP, I'm expressing a belief about an unproven conjecture. The fact that no one has demonstrated an algorithm for an NP-hard problem in polynomial time, is not enough to reject P = NP, even if an arbitrary large time window is used, a proof is still required.